Home
Class 11
MATHS
If positive numbers a ,b ,c are in H.P....

If positive numbers `a ,b ,c` are in H.P., then equation `x^2-k x+2b^(101)-a^(101)-c^(101)=0(k in R)` has (a)both roots positive (b)both roots negative (c)one positive and one negative root (d)both roots imaginary

Promotional Banner

Similar Questions

Explore conceptually related problems

If a ,b ,c in Ra n da b c<0 , then equation b c x^2+2(b+c-a)x+a=0h a s (a)both positive roots (b)both negative roots (c)real roots (d)one positive and one negative root

If alpha, beta in C are distinct roots of the equation x^2-x+1=0 then alpha^(101)+beta^(107) is equal to

If b > a , then the equation (x-a)(x-b)-1=0 has (a) both roots in (a ,b) (b) both roots in (-oo,a) (c) both roots in (b ,+oo) (d)one root in (-oo,a) and the other in (b ,+oo)

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

If a ,b and c are in A.P. and one root of the equation a x^2+b c+c=0 is 2 , the find the other root dot

If a,b and c are distinct positive real numbers in A.P, then the roots of the equation ax^(2)+2bx+c=0 are

If a ,b ,c ,d in R , then the equation (x^2+a x-3b)(x^2-c x+b)(x^2-dx+2b)=0 has a. 6 real roots b. at least 2 real roots c. 4 real roots d. none of these

For a , b , c non-zero, real distinct, the equation, (a^(2)+b^(2))x^(2)-2b(a+c)x+b^(2)+c^(2)=0 has non-zero real roots. One of these roots is also the root of the equation :

If a, b, c are positive real numbers such that the equations ax^(2) + bx + c = 0 and bx^(2) + cx + a = 0 , have a common root, then

Both the roots of the equation (x-b)(x-c)+(x-a)(x-c)+(x-a)(x-b)=0 are always a. positive b. real c. negative d. none of these